Stopping program from running in the background.

I have a Droid 2, I'd like to know what the difference between Force Stop (in Manage Applications) and Kill (in Advanced Task Killer)is? Do they both stop apps from running in the background or is one better or safer to use then the other, or do they not have anything to do with each other?

In Android, processes and Applications are two different things. An app can stay "running" in the background without any processes eating up your phone's resources. Android keeps the app in its memory so it launches more quickly and returns to its prior state. When your phone runs out of memory, Android will automatically start killing tasks on its own, starting with ones that you haven't used in awhile.
The problem is that Android uses RAM differently than, say, Windows. On Android, having your RAM nearly full is a good thing. It means that when you relaunch an app you've previously opened, the app launches quickly and returns to its previous state. So while Android actually uses RAM efficiently, most users see that their RAM is full and assume that's what's slowing down their phone. In reality, your CPU—which is only used by apps that are actually active—is almost always the bottleneck.
Why Task Killers Are (Usually) Bad News

Apps like Advanced Task Killer, the most popular task killer in the Market, act on the incorrect assumption that freeing up memory on an Android device is a good thing. When launched, it presents you with a list of "running" apps and the option to kill as many as you want. You can also hit the Menu button to access a more detailed "Services" view, that lists exactly which parts of each application are "running", how much memory they take up, and how much free memory is available on your phone. This set-up implies that the goal of killing these apps is to free up memory. Nowhere on the list does it mention the number of CPU cycles each app is consuming, only the memory you'll free by killing it. As we've learned, full memory is not a bad thing—we want to watch out for the CPU, the resource that actually slows down your phone and drains your battery life.
Thus, killing all but the essential apps (or telling Android to kill apps more aggressively with the "autokill" feature) is generally unnecessary. Furthermore, it's actually possible that this will worsen your phone's performance and battery life. Whether you're manually killing apps all the time or telling the task killer to aggressively remove apps from your memory, you're actually using CPU cycles when you otherwise wouldn't—killing apps that aren't doing anything in the first place.
In fact, some of the processes related to those apps will actually start right back up, further draining your CPU. If they don't, killing those processes can cause other sorts of problems—alarms don't go off, you don't receive text messages, or other related apps may force close without warning. All in all, you're usually better off letting your phone work as intended—especially if you're more of a casual user. In these instances, a task killer causes more problems than it solves.What You Should Do Instead

That said, not all apps are created equal. Many of you have used task killers in the past and actually found that after freeing up memory, your phone works a bit better. It's more likely that this is because you've killed a bad app—one that was poorly coded, and (for example) keeps trying to connect to the internet even when it shouldn't. Any performance increase you experience is more likely because you killed the right app, not because you freed up loads of memory (or, in many cases, it's just placebo). Instead of killing all those apps, find out which ones are actually causing the problems. If you really know what you're doing, you may benefit from using a task killer to stop the one or two inefficient-but-loved apps on your phone.
Note, however, that this is still a contested notion. A lot of developers (including ROM builder extraordinaire, Cyanogen) will not even look at your bug reports if you're using a task killer. In this humble blogger's opinion, your best bet is to stay away from regular task killer usage entirely. If you absolutely have to have that one battery-killing app on your phone, though, kill away—just be aware that when you experience a recurring Android bug later on, the task killer may be at fault. Of course, you can just stop using it to determine whether that is or isn't the case.